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By J. E. Hilliard

AS is well-known, the length per unit volume, Lv, of any lineal feature (such as grain edges in a polycrys-talline specimen) can be estimated from a count of the number of point intersections with a random plane of polish. Specifically:' Lv = 2NA in which NA is the expected number of intersections per unit area of the plane. As with all other measurements in quantitative metallography, the estimation of Lv is subject to a sampling error, the magnitude of which will depend on the number of observations. The analysis is usually performed by counting the number of intersections falling within a closed test figure of known area applied to a succession of different areas on the plane of polish. The test figure can be drawn directly on the screen of a projection microscope or else superimposed on the image of the structure by means of a reticule in a focusing eyepiece of an ordinary microscope. The use of micrographs is very inefficient unless, as in the present study, these are also needed for some other purpose. Consider an analysis in which n applications are made of a test figure within which the expected number of intersections is N. The expected total number of intersections counted is then given by NT = nN If (N) is the standard deviation in N for one application of the figure and if the latter is applied to non-overlapping regions so that the N's are independent in the statistical sense, then the standard deviation in Nt is given by: a(NT) = a(N)vn Eliminating n from Eqs. [2] and [3] we obtain: Thus, k will be a constant for a given specimen and test figure. From Eqs. [ I] and [4] we find As is to be expected, therefore, the fractional error in the estimation of Lv is inversely proportional to the square root of the total number of intersections counted. It is very desirable to have at least a rough estimate of k before starting an analysis, since it will then be possible to decide in advance by use of Eq. [5J how many counts should be made in order to achieve the desired accuracy in Lv. Without such information the investigator, unless lucky, will either do needless (and tedious) work or else obtain a result with too large an error. It is very easy to calculate k for the limiting case of N — 0, i.e., when the test figure is vanishingly small. In this case there is a negligible probability of two or more intersections falling within the figure. There are therefore only two possible outcomes: a count of one with a probability of, say, p and a zero count with a probability of (I-p). Thus and Therefore: We might expect k to depend on N and therefore on the size of the test figure. Such a dependence was observed2 in the analogous case involving the estimation of grain-boundary area per unit volume by a count of the number of intersections of a test circle with traces of the boundaries on the plane of polish. In this case the theoretical value of k at the limit N — 0 was 1.41. It was also predicted that k would display an initial sharp decrease with increasing N. Experimentally, k was observed to decrease to a value of 0.62 at N - 6 and thereafter remain approximately constant. Furthermore, the value of k for N > 6 was found to be insensitive to the form of the structure provided no pronounced anisotropy or grain-size variation was present. In order to determinewhether k would exhibit a similar dependence on N in the estimation of grain-

Jan 1, 1967

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.

By T. J. Koppenaal

The surface slip line structure has been investigated by optical microscopy during the easy glide deformation of Cu-A1 single crystals as a function of composition, testing temperature and prior thermal treatment. The slip line structure in alloys of 2.5 or less at. pct Al is similar to pure copper, while alloys of 5 or more at. pct Al show slip tracings typical of a brass. Cross slip is observed in the "a-brass type" crystals and the amount of this type of slip increases rapidly with aluminum content. The cross slip tendency in 14 at. pct Al crystals is signicantly higher when tested at 150°C as compared to 4.2" and 77°K. In addition, cross slip is more pronounced in this alloy in the furnace cooled condition than when quenched from 450°C. The cross slip behavior is analyzed in terms of existing models for this type of deformation. In two previous investigations, reports of yield points1 and solid solution strengthening2 in Cu-A1 single crystals have been given. This paper enlarges upon the brief description of the slip line structure discussed in these reports. Since the easy glide slip line pattern of copper changes markedly with the addition of -30 pct Zn (-brass),3 a study of slip lines as a function of solute additions in Cu solid solutions should help to explain some of these differences. In addition to composition variables, slip lines have also been studied as a function of testing temperature and prior thermal treatment. PROCEDURE The slip line observations were made on single crystals of 0.5 to 14 at. pct Al using a light microscope. Details concerning the preparation and basic testing procedure are given elsewhere.' Prior to testing, each crystal was homogenized at 900°C for 24 hrs, furnace cooled, and electrolytically polished in a 60 pct phosphoric acid solution. The strain rate was-5 X 10 sec-I in each case. Unless otherwise stated, all observations reported upon here were made during the early stages of easy glide. RESULTS AND DISCUSSION The maximum magnification generally used was 1000X, and slip lines could be resolved down to about 105 cm (1000A). This resolution is appreciably less than obtainable with electron microscopy replica techniques where the replication can resolve slip lines down to about 40 A. Thus, while many qualitative features could be studied, the type of quantitative data obtainable with an electron microscopy replica study could not be made. Crystals containing 0.5 and 2.5 at. pct Al deform much like pure copper exhibiting a high density of fine slip lines that cover the entire gage length of the specimens. Fig. 1 shows the surface slip line pattern in a 2.5 at. pct A1 extended 0.01 shear strain at room temperature. Crystals having 5 to 14 at. pct A1 showed appreciably coarser slip lines that were generally concentrated at one end of the gage length. During easy glide these coarse slip lines propagate along the gage length in a manner similar to that observed in a-brass single crystals by Piercy, Cahn, and cottrel14 and refered to by them as a Lüders band propagation. Fig. 2 shows a typical area of these coarse slips in a 14 at. pct A1 crystal after a room temperature shear strain of 0.01. Two slip systems were apparently active. Using a method described by Cullity, the angles, between the specimen axis and the normals of the primary and secondary slip planes were determined to be 50 and 84 deg, respectively. 'From the Laue photograph, was 52, 81, 66, and 30 deg for the primary, cross, conjugate, and fourth slip planes, respectively. The secondary active plane in Fig. 2 is thus established as the cross slip plane, and the operative slip system is evidently the cross slip system, e.g., slip

Jan 1, 1963

By F. Brons, V. E. Marting

In the past, other authors.1, 2 have studied the influence of a skin effect on the productivity of a well. This skin effect, expressed by the skin factor S, is considered to be caused by a thin layer of impaired permeability immediately around the wellbore and extending vertically over the whole productive interval penetrated by the well. The skin factor S is defined as follows. Based on this, the impairment in productivity caused by a skin can be expressed by the fractional loss in productivity I, which is the loss in productivity divided by the total unimpaired productivity. For compressible flow in a stabilized well which drains a circular area of radius re, 1 is given by The present paper deals with a different kind of productivity impairment. Consider a well in which part of the productive formation is blocked off completely, either by incomplete penetration or by exclusion of parts of the productive zone by blank casing. In Fig. 1 (A, B and C), three examples are shown. Fig. 1(A) shows the situation where a well only partially penetrates the formation. This often is done to combat the actual or imagined danger of bottom-water coning. Fig. 1(B) shows a well producing from only the central portion of a productive interval. This type of completion is sometimes used where both water and gas coning are a problem. Although the case of a well producing through perforated casing cannot be treated in a manner similar to the previous two cases (where radial flow in the horizontal plane is assumed), Fig. 1(C) shows several intervals open to production and qualitatively describes this case (as will be discussed later). To study the loss in productivity in all these cases, two parameters are introduced which fully determine the impairment. The first is the penetration ratio "b," i.e., the total interval open to fluid entry divided by the total thickness of the productive zone. The second is the ratio hlrw. In this ratio, rw is the wellbore radius. The definition of h is more cumbersome. In Fig. 1(A), h is the thickness of the total productive interval. The streamline configuration for this case of partial penetration is basic to the other two cases considered (Views B and C of Fig. 1). It will be obvious from Fig. i (A) that the flow lines in the uppermost portion of the formation will be essentially horizontal, while those in the lower portion will curve upward toward the well. In Fig. 1(B), with only the middle portion of the zone open to production, the streamline configuration. of the upper half will be an exact mirror image of that in the lower half of the zone. Hence, for the case illustrated in Fig. 1(B), h is defined as one-half the total sand thickness. It follows, then, that in Fig. 1(C) h is one-half the distance between corresponding points in adjacent intervals. (In gun-perforated casing, h would be one-half the distance between perforations.) In a paper by Nisle4 and a paper given by the present authors5, the mathematical theory was developed for the cases under consideration. In the present publication, the emphasis is put on the results of these studies; consequently, the equations derived in Refs. 4 and 5 will be omitted, for the most part. The pressure drop p in a well producing from only a portion of the total formation thickness can, in analogy with Eq. 1, be expressed by Numerical solution of Eq. 5 by use of the IBM 650 leads to the following important conclusions. First, during a short period after starting production (usually on the order of a few minutes), the function p(b) is given by

By J. A. Musselman, P. F. Gnirk

A study was made of indexed penetrations by a single dull bit tooth under statically applied loads into rock subjected to confining pressures from atmospheric to 5,000 p.si and atmospheric pore pressure. Experimental results obtained with a 45" wedge tooth over the above range of pressures are presented for two limestones and a sandstone, a variely of indexing distances and two degrees of tooth dullness. The optimum distance between successive bit-tooth penetrations required for maximum rock damage and chip formation decreases substantially with increa.sing confining pressure above the brittle-to-ductile transition pressure of a particular rock. However, the distance remains approximately constant for a variation in confining pressure below the transition pressure. At a given confining pressure, the bit-tooth force required lor chip formation is constant for indexing distances greater than optimum, but generally decreases linearly with decreasing indexing distance for distances less than optimum. The chip-formation force data obtained at confining pressures for which the chip-generation mechanism is macroscopic-ally of a pseudoplastic nature compare favorably with previous theoretical results for indexed dull hit-tooth penetrntion into an idealized, rigid, perfectly plastic rock. INTRODUCTION To study the cutting action of a roller-cone bit, the interaction of a penetrating bit tooth with craters formed in a rock surfacc by the passage of previous bit teeth must be considered. Current knowledge of the basic mechanics of bit tooth-rock intcract:on under simulated borehole environmental conditions has been extensively reviewed.',' Particularly of current interest are the effects of bit-tooth shape, distance between successive penetrations and differential pressure at the rock surface on the extent of the interaction. Pertinent to this paper are results of an experimental investigationb f the interaction between successive penetrations by sharp, wedge-shaped bit teeth. It was demonstrated that both bit-tooth angle and differential pressure influence the extent of rock damage between successive bit-tooth penetrations. Specifically, the optimum or minimum distance between successive penetrations required for maximum interact'on or chip generation tends to decrease with decreasing bit-tooth angle and increasing differential pressure. In addition, at differential pressures on the order of 2,000 psi for four va- rieties of limestones and sandstones, the macroscopic mechanism of chip formation exhibits a transition from brittle to ductile. In this paper, experimental consideration is given to successive or indexed penetrat ons by wedge-shaped bit teeth. Since pore pressure in a rock sample is maintained at atmospheric pressure, the differential pressure at the fluid-rock interface is equal to the confining pressure. The degrees of bit-tooth dullness include teeth with flat and round apexes (Fig. 1). Of primary concern in this paper are the bit-tooth forces required for chip formation, the macroscopic mechanism of chip formation and the minimum distance between successive penetrations, i.e., optimum indexing distance required for maximum rock damage, as functions of differential pressure. Of further interest is a comparison of actual bit-tooth chip formation forces at elevated differential pressures with calculated forces from previous theoretical results4 for indexed dull bit tooth penetration into a rigid-plastic rock. EXPERIMENTAL APPARATUS AND PROCEDURE The experimental apparatus consists of a pressure vessel equipped with a piston through the side of the vessel (Fig. 2). A single bit tooth inserted in the lower end of the piston is forced at a desired rate into the rock when the ram pressure chamber is pressurized. Electrical instrumentation incorporated into the apparatus yields a graphical plot of force on the piston as a function of bit-tooth penetration or displacement into the rock. Since the piston and ram assembly are in force equilibrium for a constant confining pressure in the main vessel, the fluid volume in the vessel remains constant during bit-tooth penetration. Hence, the force resisting penetration of the tooth is independent of the force exerted on either end of the as-

By G. C. Wallick, J. S. Aronofsky

This paper presents an experimental verification of numerical solutions of the differential equation describing the transient flow of an ideal gas through a porous material including gas slip effects. Several experiments previously proposed by one of the authors are described together with the correlation of the experimental results with the numerical solutions. Excellent agreement is shown between experiment and theory, thus demonstrating the validity of both the basic assumption made in the derivation of the differential equation and of the numerical solutions of the differential equation. INTRODUCTION In a recent paper,' one of the authors has discussed a numerical solution of the differential equation describing the unsteady flow of an ideal gas through a porous material. This paper was primarily concerned with the effect of gas slip on the flow behavior. In steady state measurements, Klinkenberg2 and others have observed that the apparent gas permeability Kn of a porous material may be expressed as a linear function of the reciprocal average pressure 1/P of the form, ka = b + m/P........(1) where the intercept b is a constant for a given porous material and the slope m is a constant for a given porous material-gas combination. Aronofsky1 assumed that Equation (1) could be used to describe transient flow if P was replaced by the average pressure in an infinitesimal volume element. A number of numerical solutions of the resultant differential equation were presented and specific flow experiments were proposed as a means of testing the numerical solutions. The purpose of the present paper is to describe the results of several of these experiments and the correlation of the experimental data with the results of the numerical analysis. Reference should be made to the previous paper' for details of the mathematical and numerical analysis. EXPERIMENTAL PROCEDURE A simplified schematic drawing of the experimental apparatus is shown in Fig. 1. An 8.89 cm diameter limestone core of length L = 14.82 cm was mounted in a conventional rubber sleeve permeameter cell. The external sleeve pressure in this cell was maintained equal to 500 psig during all experimental tests, thus permitting only longitudinal flow through the core. One end of the core, X = L, was connected to an adjustable cavity of volume V as well as a pressure gauge or manometer. The other end of the core, X = 0, was connected to a Nullmatic pressure regulator which was in turn connected to a nitrogen cylinder or vacuum pump. In each experiment, the core and adjacent dead volume were charged with nitrogen to a uniform gas pressure P1. The pressure at X = 0 was then suddenly raised or lowered to a constant pressure P, and the resulting pressure buildup or pressure decline at X — L was recorded as a function of the time. The porosity + and the permeability constants m and b were determined using the transient method which was suggested by the results of the numerical analysis and which was described in the earlier paper.' The following average values for these constants were obtained as a result of 19 separate evaluations: 171 -0.259 2 0.005 md-atm; b = 0.374 5 0.008 md; and F = 0.098 ± 0.005*. It should be noted that in order that transient phenomena will be slow enough to be observed conveniently, it is desirable to use a porous material of very low permeability, e.g., less than I md. Moreover, it is in this low permeability range that the gas slip effects are most significant. Thus, such a low permeability sample is very suitable for use in an experimental verification of the numerical solutions previously described.

Jan 1, 1955

By V. J. Kniazeff, S. A. Naville

The problem of unsteady-state condensate-gas flow through porous media leads to a set of second-order non-linear partial differential equations. Such a set of equations is numerically solved in the case of radial two-phase flow around a well, taking into consideration both the thermodynamical properties of the fluid and the mechanical properties of the reservoir. The fluid properties, reflecting the PVT relationship of the gaseous and liquid phases, are expressed by using the partial specific masses of the two main separator products in these phases. The flow properties of the reservoir rock are expressed by the generalized Darcy's law for the liquid phase and by a quadratic relationship between the rate of flow and the pressure gradient for the gaseous phase. The numerical solution of the equations for pressure and saturation US radius and time is worked out through programs written for a computer. The evolution of bottom-hole pressures, well productivities or- deliverabilities and effluent compositions with the depletion of the reservoir is easily derived. The application to the Saharian gas-condensate field Hassi R'Mel led to a better understanding of the drainage mechanism. A zone of fairly high liquid saturation develops around the wells, reducing the effective permeability, and represents a loss of condensible products in addition to the PVT-like retrograde condensation. lnside this zone, near the well, the deviation from Darcy's law for the flow of the gaseous phase governs the well deliver-ability. A back-pressure test has been computed and correlates with the field results. INTRODUCTION Two-phase flow of volatile hydrocarbons, like condensate gas or light crude oil, may be treated as the flow of a binary mixture by an arbitrary division of the chemical components into two groups. This is translated into two equations of mass continuity, which constitute a set of relation- ships for the pressure and the saturations vs the space coordinates and the time. The equations contain the laws governing the composition and the motion of the phases. The problem so defined is solved with the assumption that the compositions of the phases at any pressure are respectively the same as those observed in a PVT measuring cell under differential liberation. In a first series of computations, it was assumed that the flow obeys the generalized Darcy's law. A satisfactory representation of the retrograde condensation around the well was thus obtained. In addition, the trend toward decreasing effective permeabilities was obtained, and the computed composition of the effluent checked the laboratory values. However, it has not been possible within this basic assumption to represent the non-linear relationship between the production rate and the bottom-hole pressure drawdown as observed for gas wells in the field. Following the advice of A. Houpeurt it was decided to consider the relative permeability to gas as a function of the velocity of the gas Phase.1 The necessary physical determinations were made by E. COstaséque using a method devised by A. Houpeurt and R. Iffly. As numerical processing of the equations progressed, several difficulties were encountered which were overcome through collaboration with the computer manufacturer. This mathematical model of two-phase flow in porous media had been primarily intended for and extensively applied to the case of the Hassi R'Mel gas-condensate field, operated by SN Repal for SEHR, a joint subsidiary of SN Repal and CFP (A). The programs have also found their applications to forecast the behavior of several fields in the Sahara area containing light and volatile hydrocarbons. BASIC EQUATIONS We will consider a zone in the porous reservoir where the flow properties and the in situ composition of the fluids can be assumed to be uniform. A part of the equations of transient flow can be written with the specific gravity of the fluids being taken equal to the sum of the contributions due to the

Jan 1, 1966

By W. L. Phillips

Single crystals of aluminum, brass, and copper oriented for (100) and (110) slip were extended at 25°, 400°, and 600°C in simple shear. Aluminum specimens oriented for nonoctahedral slip began to shear at a higher critical resolved shear stress than specimens oriented for octahedral slip. Parabolic stress-strain curves were obtained from zero strain. The initial rate of parabolic hardening was lower for specimens sheared on the (100) plane in a close-packed direction <110>, than for specimens sheared in a nonclose-packed direction <100>. metallographic evidence, however, showed that all slip traces could be explained in terms of (111) <100> slip. All attempts to cause nonoctahedral slip in copper and 70-30 a-brass single crystals were unsuccessful. Instead of shearing, the crystals bent, allowing {111} type planes to come into action. NONOCTAHEDRAL slip in aluminum has been reported under three different conditions: first, as the main mode of slip in tension experiments at elevated temperatures;&apos;-&apos; second, as the main mode of slip in direct shear experiments at room temperat~re; and third, as a minor mode of deformation, i.e., as cross-slip, in tension, shear, and bicrystal experiments at room and elevated temperatures."-l2 However, as far as the author knows, nonoctahedral slip has not been reported in either copper or 70-30 a-brass. The present study was undertaken to determine whether nonoctahedral slip could be obtained in aluminum, brass, or copper at room or elevated temperatures when the shear stress was approximately constant over the cross-section, a maximum at the center, or a maximum at the surface. EXPERIMENTAL PROCEDURE A detailed description of the crystal preparation and shearing apparatus has been given previo~sly. Cylindrical crystals 1/2 in. in diam and 8 in. long were grown from the melt in a temperature-gradient furnace. The aluminum contained 0.001 pct Zn, 0.001 pct S, and 0.001 pct Fe; the 70-30 brass contained 0.015 pct Pb, 0.001 pct Fe, 0.01 pct Ni, 0.02 pct Sn, and 0.005 pct Se; the copper was certified OFHC of 99.98 pct purity. All samples were electropolished prior to testing. The shear apparatus was a modified Bausch type. The strain sensitivity was 4 x lob4 Load was applied by clamping the rods attached to the shear plates in an Instron tensile machine. The rate of loading was 0.02 in. per min. In all cases a 1/8-in. gage length was used. For the tests performed at 400° and 600°C the shear plates, collars, and rods were made of stainless steel. These elevated-temperature tests were performed in an argon atmosphere. A) Aluminum at Room Temperature. Values of a and ß for the various slip planes and slip directions investigated are shown in Table I where a is the complement of the angle between the specimen axis and the slip direction, and ß is the angle between the specimen axis and the normal to the shear plane. The shear stress is a function of a (assuming ß - 0);10 when a is less than 27 deg, the shear stress on the slip plane for which the specimen is oriented has a maximum at the center of the crystal; at a = 27 deg the shear stress is constant across the slip plane; for a greater than 27 deg the shear stress is a minimum at the center. Fig. 1 shows the stress-strain curves for specimens cut from crystals 1, 2, and 5, which were sheared on the (010) plane in the [loll direction at room temperature. These three crystals have shear-stress distributions corresponding to the three dif-

Jan 1, 1962

By I. R. Dunlap, R. F. Burdyn, F. D. Patchen

The composition and properties of a new type of cementing mixture are discussed. In these compositions, API Class A or C cements are added to n stable water-in-oil emulsion instead of the crsual water. The cement disperses in the oil phase and remains out of contact with the water under normal conditions of mixing and storage. At higher temperatcrres, such as those encountered down-hole during placement, the emulsion breaks and cement hydration can then proceed. An extremely low filtration rate is obtained; the major part of the filtrate is oil. Thickening times of the mixture may be increased to meet the 18,000-ft casing cementing schedule by varying the amount of emzilsifier. As in conventional Portland cement mixtures, high-temperature strength retrogression can be overcome by addition of silica flour. Results of several field app1ication.r show that mixing presents no diffculty if emulsion blenders are used and the emulsion is prepared beforehand. INTRODUCTION Water-in-oil emulsions., in which oil is the continuous or external phase and in which water exists as discrete droplets, have for some time been used successfully in drilling muds to reduce filtration loss.1,2 Applied to cement slurries, the same results are obtained; i. e., the fluid-loss is greatly reduced. In addition, thickening times may be extended, lower densities and strengths obtained, and water-base borehole fluids more easily displaced without contamination of the cement. A low filtration rate is often a desirable property in oil well cements since loss of fluid increases placement difficulties and may also cause damage to water-sensitive producing formations.&apos; In the casing cementing operation where the cement slurry is pumped into the narrow annulus between open hole and casing, rapid loss of fluid to a porous formation can cause the slurry to thicken and plug the annulus before the desired fill is obtained. Where a casing or a liner is cemented against a productive formation and the well completed through perforations, the fluid lost between the time the cement first contacts the formation and the time a set is obtained may invade the zone past the depth of the perforations. If the sand contains a material which will swell upon contact with cement filtrate, permanent damage may result. Previous methods for reducing the fluid-loss of cements have employed bentonite4 as an additive, usually with a lignosulfonate as a dispersant, or a derivative of some naturally occurring polymeric material such as cellulose ether." Oil emulsion cements have also been proposedv or fluid-loss reduction, but these have been of the oil-in-water type. Bentonite cements have been used most widely and have been successful in reducing incidence of premature setting of cement attributable to loss of water by filtration. It is the purpose of this paper to describe preparation and properties of a water-in-oil emulsion cement and to relate procedures followed and results obtained in several field applications. DESCRIPTION OF SYSTEM AND MECHANISMS A water-in-oil emulsion cement is prepared by adding an API Class A or C cement to a stable water-in-oil emulsion. Fig. 1 is a photomicrograph of this emulsion before addition of cement. Here the droplets are water and the surrounding medium is diesel oil. High emulsion stability is indicated by the small droplet size [1-5 microns], and by their uniformity.&apos; To form a stable water-in-oil emulsion as illustrated, several conditions must be met. A predominantly hydrophobic emulsifier must be present in sufficient concentration to produce a strong interfacial film; initially, the phase volume ratio (the water-to-oil ratio) must be low;

By R. Lagneborg, R. Gullberg

An X-ray method for determinig volume fractions of phases in textured materials has been developed. The method involves measurements of the integrated intensities of reflections of each phase for one single orientation of the sample. The method was checked by evaluating the phase contents in samples from two stainless Cr-Ni steels containing austenite and ferrite in known amounts. In the present case measurements of about five reflections from each phase were required. The agreement between calculated and known volume fractions was found to be very close. AN X-ray diffraction method is often employed for determining the amounts of two or more phases in a material. The details of the method have been described at several instances.&apos;" In short, the method is based upon the fact that the integrated intensity of a reflection is directly proportional to the volume fraction of the phase considered. In principle, the method only requires the measurement of the intensity of one reflection for each phase. The most severe shortcoming with this method is that it disregards influences from preferred orientation in the material. In a diffractometer, where this type of analysis is most conveniently carried out, the geometry is such that the diffracting planes for a specific Bragg peak are all parallel to the surface of the specimen. This implies that it must be required that the occurrence of the diffracting planes parallel to the specimen surface must be as frequent as for any arbitrarily oriented physical plane of the sample. This requirement will generally only be fulfilled for a material free of texture. Since all materials in reality always exhibit a preferred orientation to some extent. the deficiency of the method is quite serious. In cold-deformed material the texture is appreciable, but also annealed material will in many cases display a considerable texture. The problem of quantitative phase analysis in textured material is one of obtaining the integrated intensity averaged over all orientations of the specimen with respect to the X-ray beam. Lopata and ~ula~ have shown that this can be accomplished by integration of intensities over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. Hence, in this method the average integrated intensity for a specific reflection is obtained by directly determining the intensity for a sufficient number of physical orientations of the sample. However, since an excess of diffracting planes in a certain surface plane necessarily must be accompanied by a deficiency of another type of diffracting plane, it appears to be possible to obtain the correct average intensity for a specific diffracting plane by performing an appropriate averaging of intensities belonging to a large number of diffraction planes of different hkl when all intensities have been produced from one single orientation of the specimen surface. In the present work such a method has been attempted and tested experimentally for two stainless Cr-Ni steels containing austenite and ferrite. 1) THEORY The expression for the integrated intensity of a Bragg reflection diffracted from a phase in a polycrys-talline sample in a diffractometer is: where C is a constant only dependent on the incident X-ray power and the diffractometer geometry, v the volume of the unit cell, F the structure factor, m multiplicity of the diffracting plane, L Lorentz factor, P polarization factor, e-2 temperature factor, p average linear absorption coefficient of the irradiated vO1umej and V volume fraction of the phase &apos;Onsidered. Hence, the factor R in the abbreviated form of Eq. [I] can be calculated and depends only on 0 and the diffracting plane {hkl}. For an alloy containing two phases, a and y, we can write

Jan 1, 1967

By F. W. Jessen, G. F. Sears

Cavities in massive salt for the purpose of storage of liquid hydrocarbons have assumed a prominent position in recent years. This paper describes a program to facilitate leaching operations for the formation of specifically shaped storage cavities. Various forms and sizes of cavities may be possible through use of the techniques developed. INTRODUCTION The creation of large under ground storage facilities for natural gas and liquified petroleum gases has been practiced for many years. Use of cavities obtained through solution of salt for this purpose is a fairly new and novel approach, but has gained increasing importance due mainly to the economics of this type of mining operation opposed to hard rock mining or surface and pit storage.1 The idea of controlling the shape of any cavity dissolved from massive salt has not been a prime consideration of companies engaged in the formation of storage space. This has been due mainly to an insufficient knowledge of the mechanics of the leaching process and a dearth of published information dealing with both the desirability and ease of control possible for this type of operation. Two distinct advantages are readily ascertainable. From a stability standpoint (i.e., the ability of the completed cavity to withstand stress imposed by overburden pressure and lateral tectonic stresses) a controlled cavity may be generated which will yield the most favorable attitude to these external forces and remain in operable use for longer periods of time.2 A second advantage is that for a given volume, a sphere (which is one controlIed shape possible) represents the minimum surface area exposed. This may become more important in the future when dealing with refrigeration and product losses in underground cavities. The basic solution mining process, without regard for controlling the final shape, is quite simple in that the equipment and materials required to dissolve a cavity in a salt dome or layered salt section are a source of fresh water, a circulating pump, several strings of tubing and a means of disposal of the return brine. To add control measures involves the use of an inert blanket material above the position at which solution proceeds. Initially the annulus of the largest wash pipe is filled with this blanket down to the top of the proposed cavity. The bottom of the proposed cavity is determined by the depth of the original drilled hole or a blanking plug. The blanket material is added incrementally in stages and displaces the water in the enlarging cavity downward. Where the blanket material has displaced the water, no further solution takes place. The rate at which to add this controlling blanket material so as to be able to form specifically shaped cavities of any particular size is of considerable importance. THE PROBLEM It is desirable to have as much information as possible as to the behavior of the mining operation since visual observation obviously is impossible. It would be advantageous, for example, to have a step-by-step program showing how much salt is to be removed, at what rate and the time required. This type of program would facilitate procurement of surface equipment and provide for proper management of manpower requirements, as well as yield a host of intangible benefits. As mentioned earlier, only rule-of-thumb estimates were available until recently and made this type of pre-planned operation haphazardous at best. Recent work3-&apos; has done much to clear up the ambiguities and inaccuracies attendant to solution mining of salt and has helped to place the operation on a more scientific basis. This study attempts to correlate much of the information thus far developed into a complete mining program; to extend the idea of controlled solution mining to include not only spheres, but solid conic sections of the ellipsoidal variety; and to refine the computation of the rate of removal of salt during the various stages of mining. Dommers3 and IIemson4 made extensive laboratory

Jan 1, 1967

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"&apos; and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By Larry Kaufman

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski&apos;s method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6&apos;7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6&apos;7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann&apos; suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in &apos;K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1&apos; values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This

Jan 1, 1962

By A. R. Marder

Fe-C alloys have been investigated at temperatures below the eutectoid transformation to determine whether the superplasticity phenomenon exists for these materials. As a result of void formation at the carbide-ferrite interfaces that led to void coalescence and premature failure, the large elongations characteristic of superplustic matem&apos;als did not develop. It had generally been assumed that the conditions for obtaining superplasticity include: a) T/Tm =0.5, b) a strain rate sensitivity of the flow stress that results in m s 0.3, and c) fine-grain structure. Although superphsticity was not observed in the alloys studied, stress-strain rate measurements indicated that an additional condition for the existence of superplasticitv in Fe-C allovs is that the fine-wain structure be equiaxed in agveement with previous results on Zn-Al al1oys. MANY investigations have been made on the hot deformation of iron-base alloys in order to obtain an understanding of the variables that may affect high-temperature strength and ductility.&apos;-6 However, only a few papers have studied the effect of carbon content on the high-temperature properties of iron-base alloys. Peretayat&apos;ko and Zaikov and Wallquist and carlen4 studied the effect of carbon on strength in the y temperature range, and recently Robbins, Shepard, and sherby6 studied the influence of carbon on the torsional behavior of iron in the a and cu-plus-cemen-tite temperature ranges. In addition to studying hot deformation behavior, current investigations have also been concerned with the phenomenon of superplasticity in nonferrous materials, and, in particular, ferrous alloys. Superplasticity is identified by the increased resistance to necking that results from a high strain rate sensitivity of the flow tress. ackofenr proposed the strain rate hardening coefficient m = d log a/d log e as a measure of strain rate sensitivity and showed that m must be "-0.3 for superplasticity to exist. In addition, a fine-grained microstrcture,- a eutectic or eutectoid ornosition,- and a test temperature in the creep range (TITm > 0.5)" have also been advanced as necessary conditions for superplasticity. Although many workers""23 investigated superplasticity associated with the allotropic transformation in iron and the eutectoid transformation in steel, and recently chadler " and orrison have studied superplasticity in the a - y phase region, no one has measured the superplastic effect in the a + cementite temperature region. Therefore, the purpose of this investiga- tion was to determine the effect of carbon content, microstructure, and test temperature on the strain rate sensitivity of Fe-C alloys at temperatures below the eulectoid transformation. EXPERIMENTAL PROCEDURE Fe-C alloys with carbon contents of 0.2, 0.4, 0.6, 0.8, and 1.0 wt pct were prepared as 100 lb 54 in. ingots by vacuum-induction melting. The compositions are listed in Table I. All the ingots were soaked at 2100°F for 2 hr prior to rolling to 4 in. plate. The minimum finishing temperature for rolling was 1800°F. The plate was sheared in 10-in. lengths and tensile bars were rough-machined prior to heat treatment. The samples were heat-treated according to the schedule in Table I1 in order to obtain a fine-grained microstructure consisting of finely dispersed carbides in a matrix of small ferrite grains. All the tensile specimens were heat-treated prior to finish machining, and tensile testing was accomplished on an Instron machine in conjunction with a clamshell furnace. The buttonhead specimen configuration is shown in Fig. 1. An inert atmosphere, helium, was maintained during testing with a steel tube shroud in a bell jar arrangement. Predried helium was continually purged over the buttonhead specimens and exhausted through ceramic fiber at the bottom of the tube to keep oxidation at a minimum and to prevent

Jan 1, 1970

By D. L. Albright, G. A. Colligan

An investigation has been conducted to determine the nature of the crystallographic substructure of nickel and a 1.0 wt pct Ag-Ni alloy which had been undercooled 105°C prior to solidification. A rotating back-reflection X-ray technique and modified Weissmann diffractometer were used to orient single-crystal sections from these poly-crystalline ingots and to determine the substruc-tural features of these single crystals, The sub-grain size in the pure nickel ingot is 0.5 mm diam while the silver-doped nickel subgrain size is only 0.1 mm diam. The misorientation between adjacent subgrains is approximately 1 deg of arc in both ingots, and the spread of orientation of sub-grains about the mean orientation of the crystal is 5 deg of arc in both ingots. The addition of silver results in a stable impurity substructure which is preserved during isothermal solidification and subsequent cooling to room temperature. In the absence of silver the initial impurity substructure is destroyed by dislocation interactions which produce a secondary substructure which grows to a size five times larger than the initial substructure. THE process of undercooling a metal entails cooling of the molten sample below the equilibrium freezing point without the occurrence of solidification, i.e., by exercising proper constraint over the experimental variables contributing to nucleation in the melt. The current work of walker1 and Colligan Metal reports undercooling large continuous samples of nickel by imposing appropriate restrictions upon the parameters of solidification. The silver-nickel equilibrium diagram3 reveals the presence of a monotectic reaction at 1435°C. At this temperature the maximum solid solubility of silver in nickel is approximately 3 wt pct, but this solubility decreases with decreasing temperature and the solute is rejected as a silver-rich liquid phase at temperatures below 1435°C. Thus, the 1.0 wt pct solute should be held in solution during undercooling and solidification and subsequently precipitate as a silver-rich liquid phase at grain and subgrain boundaries following solidification during cooling below 1435. This assumes no solute segregation sufficient to cause the monotectic reaction. One would expect this second phase to inhibit grain and subgrain growth by retarding dislocation motion after solidification is complete. The effectiveness of silver addition in growth retardation of high-angle grain boundaries has been demonstrated by Colligan and suprenantS4 The principal [l00] dendrite growth directions in a 2 wt pct Ag-Ni alloy undercooled 53 all radiated from the nucleation site. A similar pure nickel ingot undercooled 59°C exhibited a random orientation of [l00] dendrite directions with respect to the nucleation site. Since undoped nickel ingots do not retain any evidence of the casting or solidification texture and silver-doped ingots do retain this texture, it is reasonable to assume that considerable grain growth has taken place in the pure nickel. These particular experiments were performed in order to reveal the differences, if any, in the features of the crystallographic substructure of undoped undercooled nickel and silver-doped undercooled nickel. 1) EXPERIMENTAL PROCEDURE Data are reported on selected specimens from two massive (approximately 260 g) undercooled ingots of nickel. One ingot consisted of electrolytic nickel and the other of this same material with 1.0 wt pct addition of high-purity silver. Powder patterns were taken of both the as-received and as-solidified materials; in all cases the reflections recorded were attributable to the individual elements nickel and/or silver. Fig. 1 is a. schematic diagram of the apparatus employed for the undercooling experiments. The equipment consists in part of a fused silica crucible for containing the charge. A fused silica tube encloses the system, which is covered by a brass cap to permit partial sealing of the inert atmosphere. This cap contains a hole through which a Pt-Pt 13 pct Rh thermocouple is inserted for temperature measurement. The charge is inductively heated under a purified argon atmosphere.

Jan 1, 1963

By H. S. Price, J. E. Warren

Techniques for studying the performance characteristics of heterogeneous reservoirs have been developed. The effect of permeability variation on both the steady-state and the transient flow of a single fluid has been investigated. Limited comparisons with field and laboratory data have been made. The physical models studied consist of random three-dimensional arrays of homogeneous porous blocks. The permeabilities of the individual elements are assigned according to a specific distribution function; uniform anisotropy is introduced by varying the relative dimensions of the blocks. A particular model is perturbed simply by re-arranging its elements at random. The behavior of a physical model is determined by digitally solving its numerical analogue. Based on computational experiments, subject to the restrictions implied by the assumptions that were made, the following general conclusions have been drawn. 1. The most probable behavior of a heterogeneous system approaches that of a homogeneous system with a permeability equal to the geometric mean of the individual permeabilities. 2. The effects of flow geometry and anisotropy on the most probable value of the effective permeability of a heterogeneous medium are finite but not significant. 3. The permeability determined from a pressure build-up curve lor a heterogeneous reservoir gives a reasonable value for the effective permeability of the drainage area. 4. A qualitative measure of the degree of heterogeneity and its spatial configuration are obtained from a comparative study of core analysis and pressure build-up data. It has been indicated that these conclusions are predicated on the assumption that the core analysis and the pressure build-up data represent true reservoir characteristics. Common sources of error in these data have been discussed. One of the most significant problems of reservoir engineering is that of determining the nature and the disposition of the heterogeneities that inevitably occur in petroliferous formations. It is with this problem that this paper is concerned. Extensive research, both theoretical and experimental, has provided reasonable descriptions of the physical processes that are associated with primary and secondaryrecovery mechanisms. Similar progress in the fie1d of numerical analysis and the evolution of truly high-speed digital computers have made it feasible to calculate the behavior of these mechanisms under almost any environmental conditions. It appears to be logical, then, to conclude that the mechanistic performance of any reservoir can be predicted with some confidence. Unfortunate1y, a necessary condition for the validity of this conclusion is that the formation be adequately described in a macroscopic sense. This condition cannot be satisfied ill general; therefore, a frustrating situation currently exists — it is possible to compute the effect of reservoir heterogeneity on behavior, but it is not possible to specify the heterogeneity itself. In many cases, the predicted behavior of a project is so completely dominated by irregularities in the formation&apos;s physical properties that the gratuitous assumptior, of a particular form for the variation can reduce the solution of the problem to a mere tautological exercise. While all porous media are microscopically heterogeneous, only macroscopic fluctuations need be considered since the fundamental concepts of reservoir mechanics are based on macroscopic quantities. For the simplest case in which only one physical property varies from point to point, the degree of heterogeneity that is apparent depends on three distinct factors, i.e., the nature of the property&apos;s variation (frequency distribution), its disposition (spatial distribution) and the inherent stability of the mechanism being studied. Consequently, any attempt to devise an unambiguous scale of heterogeneity must take these factors into account. Since this investigation is intended to be exploratory, it will be restricted to single-phase flow because of the simplification implied; both steady-state and unsteady-state behavior will be considered. Furthermore, to keep the number of parameters

By Goldye Leeds, Marian Balicki

A SURVEY of literature reveals the scarcity of experimental evidence relating to work hardening and reannealing of silver.&apos;-&apos;" With the exception of the well-known X-ray investigation of silver and other metals by W. A. Wood? the effect of progressive cold working has not been studied. The determination of thermal stability of silver in the work-hardened state by means of isochronal or isothermal annealing has been confined apparently to very high reductions only. In the survey made, no study was encountered which endeavored to produce a complete picture of the changes in various properties due to cold working and subsequent reannealing. To fill these gaps and to assemble data that could be used for the determination of activation energies and of frequency coefficients of primary recrystallization, a systematic experimental approach, which was developed by one of the authors, has been applied to pure silver. Material and Processing The silver used was Handy and Harman fine silver, with a spectroscopic analysis at the testing stage of Cu, 0.0001 to 0.001 pct; Te, 0.0001; Pb, Si, Ca, Mg, and Mn, traces. The material was supplied in the form of a rod 0.406 in. diam and was converted into test samples according to the procedure condensed in Table I. It should be mentioned that air annealing was adopted to simulate industrial practice, though it was realized that annealing in a neutral gas or in a vacuum would be preferred. The usual precautions have been taken to eliminate any structural changes and property changes resulting from the storage of the samples prior to annealing or testing. Thus the wires were kept at the fully annealed stage, and the final wire drawing, which produced the desired degree of work hardening, was done just prior to the final annealing or testing. During the short waiting period, the samples were kept in a thermosflask filled with ice. Even with these precautions some strain-age-hardening or self-annealing could occur. To test such a possibility, wires of different reductions were prepared in the manner adopted and portions of them were immediately tested. The remaining portions were similiarly tested after different periods of storage, both at room and melting-ice temperature. Within experimental error, all samples obtained from a wire of a given percentage of reduction yielded identical values. This result qualified the material for further tests and interpretations, because it showed that either strain-age-hardening and self-annealing were absent, or that these effects fully balanced each other. The final annealing was carried out in an electric resistance furnace automatically controlled to within a 10°F. It was realized that the temperature fluctuations were greater than desired for this type of work. TO diminish the errors due to fluctuations of temperature, the hot junction of the thermocouple was placed as close to the samples as possible; the time of soaking was reduced to 15 min; and the number of samples annealed at different temperatures was increased. It will be seen from Table I that some tests were performed on the same material at rising temperature. These will be discussed elsewhere. Room temperature testing was limited to the determination of some of the mechanical properties that are known to be additive in a degree sufficient to be used for indirect study of the kinetics of the reannealing process, Tensile tests, carried out on a manually operated J. Camillon machine, accurate to within permitted the determination of the ultimate stress (U.S.1 and of the 2 in. elongation, (A,). The proof stress (d,e) has been determined from a series of bend tests carried out on a Tinius Olsen Stiffness Tester by using the offset method. This involved accurate determination for each sample of load-angular deflection curves, finding a

Jan 1, 1952

By G. R. St. Pierre, M. J. Pool, R. Speiser

The activities of chromium in solid Cr-Ti solulions contaitning from 10 to 90 at, pct Cr were measured over the temperatutre range 1250" to 1380°C. The Knzudsen effusion technique with direct weighing of the Knudsen cell was used. This was possible because the vapor pressure 0f chromium is about 600 times greater than the capor pressure of titanium so that the amount 0f titanium effusing could be neg-Lected. the activities of titanium were determined by g-raphical integration of the Gibbs-Duhertz equatiotz. The solutio~ls sllcdied exhibited positive deviations from Raoult&apos;s law, but they approached ideality as the temperature was raised from 125 to 138t C. The integral free energy of mixing was calclated from the activity values. AF has a maximum value of - 1.66 kcal a1 1390°C and a composition oj 55 at. pcl Cv. The free energy of formation of &apos;TiCr, is —0.76&apos; lzcal a1 1250°C. The heats and entropies of mixing usere determined using the second law and thus tile mlues could be in error by a considerable amount. The Cv-Ti system is not a regular solution. ThE increasing emphasis on application of various models to alloy formation and solution behavior has led to an intensified interest in the thermochemistry of alloys. In a majority of the cases where different models have been applied the alloy system used was a simple one. However, the amount of data available on more complicated systems is small and in order to fully understand the behavior of metallic solutions more experimental work has to be carried out on these systems. The Cr-Ti system is reasonably complex and even though this system was being investigated as early as 1937 by Kroll,&apos; no previous work has been done on the thermodynamic properties of either the liquid or solid state. This research was undertaken to determine the thermodynamic properties of solid Cr-Ti alloys. EXPERIMENTAL PROCEDURE The experiments on the Cr-Ti system were carried out in a water-cooled metal vacuum system. This system is composed of a brass vaporization chamber wound with copper tubing for cooling purposes, a brass liquid-nitrogen trap, an oil diffusion pump, and a Duo-Seal forepump. The pressure in the system is measured with an ionization gage. The interior of the vaporization chamber is shown schematically in Fig. 1. The Knudsen cell is supported by the molybdenum tripod, and a magnetically operated shutter is provided to protect the Pyrex sighting glass against deposition of metallic vapors in the intervals between temperature measurements. Heating is accomplished by means of a 20-kw 450-kc Westinghouse oscillator. The susceptor in this case is 10-mil tantalum seamless tubing which also forms the outside of the sample container. The remainder of the sample container consists Of an im~ervims re-crystallized alumina crucible and a 10-mil-thick tantalum lid. Two holes are drilled in the lid. The diameters of these holes were measured with the calibrated stage of a "Tukon" microhardness tester. The thicknesses were measured with a micrometer. A Leeds and Northrup disappear ing-filament optical pyrometer was used to measure the temperature. This is sighted through the smaller of the two holes in the lid and corrections for the emissivity of the sample were not necessary since the ratio bf cell length to hole diameter was large enough to insure a hohlraum. The pyrometer was calibrated at the ~~t~~~l Bureau of Standards, and the correction for the Pyrex sighting window was determined in the laboratory. The titanium used in this investigation was obtained from Mallory-Sharon and the chromium from The Union Carbide Metals Co. The reported purities were

Jan 1, 1968

By F. D. Patchen

Changes in the properties of partland cement upon the addition of fine-ground silica are discussed. Data were collected from formulations cured for periods up to 60 days at temperatures varying from 180" to 350°F. Compressive strengths, permeabilities and thickening times are compared. It is demonstrated that addition of find-ground silica in proper proportion results in a hydrated cement with superior properties above 230°F; i.e., early compressive strengths are higher and increase with additional curing, permeabilities are significantly lnrver and thickening times are increased. X-ray analysis of hydrated cement samples have been used to determine more fully the complex chemistry of these systems. Dicalcium silicate alpha-hydrate was found in all neat cements cured above 260°F. A 10 weight per cent silica addition produced a maximum amount of this phase. Xonotlite and tobermorite have been identified as hydration products at 320°F in systems containing 35 or more weight per cent silica. Formation of these components appears to be primarily responsible for the gain in strength and reduction of permeability observed after the addition of silica. INTRODUCTION For several years it has been recognized that loss of compressive strength occurs when portland cement is cured at a temperature above 250°F. This phenomenon has been called "strength retrogression". More recently it has been recognized that increased permeability usually is associated with decreased compressive strength at these temperatures. At curing temperatures above 300°F, these factors reach serious proportions. A compressive strength loss of 50 per cent between curing times of 24 hours and 14 days has been reported,&apos; and permeabilities as high as 10 md have been measured in neat cements cured at 320°F for seven days.&apos; Earlier investigators,&apos; although unsuccessful in eliminating strength retrogression, stated ". . . .it appears possible that by the proper selection of additives for cement, strength loss with age at high temperatures can be either eliminated or considerably lessened". One solution suggested was the use of a pozzolanic material, hydrated lime, and a retarder. Menze15 in 1934 discovered that portland cement containing finely divided silica possessed high compressive strengths when the curing temperature was 350°F. The use of such a composition is now an established practice in the manufacture of steam-cured cement blocks. It is reasonable to assume that the same beneficial effect can be used advantageously in high-temperature oilwell cementing operations. Ludwig first mentioned the use of sand for this purpose. Later, a portland cement containing moderate additions of silica flour and retarded with CMHEC, a cellulose derivative. was recommended for high-temperature application." These formulations have been successfully employed in the field."&apos;" This paper presents the results of a research program to test the efficacy of finely ground silica in increasing the compressive strength and reducing the permeability of oilwell cement compositions containing portland cement. Included also are X-ray diffraction patterns of powdered samples which have been used to determine some of the important chemical reactions occurring in these systems. LABORATORY PROCEDURES AND MATERIALS All compressive-strength test specimens were prepared and cured from a slurry in accordance with API RP 10B, with two modifications. A final curing pressure of 5,000 psi was maintained for a one- or three-day period; but, for further curing, pressures were reduced to the vapor pressure of water at the curing temperature. Also, the water content was varied in samples containing silica to maintain the slurry viscosity within a range of 5 to 15 poise as measured on a consistometer. Test specimens at 180°T were cured in a water bath at atmospheric pressure. At higher temperatures the specimens were cured in a steam-jacketed high-pressure curing vessel at 5,000 psi for a one- or three-day period. cubes cured for longer periods were removed from the pressure-curing vessel after 24 hours, sealed in small bombs containing water and placed in an aging oven.

By T. G. Nilan

Steels containing 0.4 and 0.8 pet C have been transformed isothermally at pressures up to 34 kbuv. Decomposilion mechanisms are so intimately related to phase equilibvia that, as the equilibria shift under high pressure, the microstruclures of the decomposition producls change, maintaining at pressure the same correspondence between a given phase equilibrium and a given microstructure as a1 1 atm. A bainitic unicvo-structure occurs in these steels at high pressure that IS observed only at 1 aim abole 1.4 pct C. This strrrcl111,e 1s ruliorzalized in terms of the effect of pressure on the transformation to lower bainite. The pressuve depetlderlce of the kinetics of pearlile formation is descrihed by an absolute rule theory amalysis. The activation volume for the transformation is 7 cu cm per mlole, which is indicative of a phase-interface transformation-rate cotntrol mechanism. This fortmulation, when expressed in terms of known solule effects on the energelics of tvansformation, gives promise of explaining the effects of alloying elemenls on hnrden-abilily, particularly that of &apos;coball. KINETIC processes in solids are functions of the primary thermodynamic variables of state: composition, temperature, and pressure. Until the development of high-pressure techniques&apos; that permitted the generation of sustained high pressure at high temperatures, metallurgical studies of such reactions were largely limited to isobaric conditions at atmospheric pressure. The data so obtained, and theoretical deductions based on these data, were necessarily incomplete For the particular case of austenite decomposition, a knowledge of the phenomenology of the reaction in terms of all the state variables should lead to a clarification of the process. This deeper understanding should facilitate a decision between conflicting theories that have been proposed to rationalize these phe- nomena. An analysis, derived from an understanding of the transformation mechanisms, may aid in the optimization of alloy steel development. The first studies of the effect of pressure on transformations in steel were made by Kulin et al. in 1952.&apos; In a study of the influence of applied stress on mar-tensite formation in a 30 pct Ni steel, they found that the martensite start (M,) was depressed 8°C per kbar* by hydrostatic pressure. Jellinghaus and Friedewold3 were apparently the first to investigate the effect of pressure on isothermal transformations above the Ms. They found that the bainite transformation rate in a 1.2 pct C, 3.8 pct Mn steel was reduced by a factor of 3 by a hydrostatic pressure of 4 kbar. In both of these investigations,2,3 the M, of the steels studied was below room temperature. Austenitizing and quenching were done at atmospheric pressure, followed by the decomposition of the metastable austenite under pressure. The maximum temperature at pressure in the bainite study3 was 350°C. Until the advent of the present high-pressure devices, it was not possible to conduct isobaric high-pressure heat treatments from austenitizing through isothermal decomposition and quenching. The exploitation of high pressure as a variable in metallurgical studies was greatly advanced by the apparatus and techniques developed by Hall4 and co-workers. Utilizing these techniques, Radcliffe et a1.5 and Hilliard6 etermined the pressure dependence of phase equilibria in the Fe-C system. Hilliard and cahn7 examined the pearlite transformation rate in an AISI 1080 steel and also in a high-purity 0.92 C Fe-C alloy at 1 atm and at 34 kbar and found a 700-fold reduction in rate at pressure in the 1080 steel but only a fivefold reduction in the high-purity alloy. In agreement with the shift of phase equilibria under pressure, the microstructures were hypereutectoid at 34 kbar pressure, whereas they are eutectoid at 1 atm. Determination of the effect of pressure on carbon diffu-

Jan 1, 1968